Problem 3. (20=10+10 points) Let Pn be the vector space of polynomials of degree no more than n. Define the linear trans

[answerhappygod]

Problem 3 20 10 10 Points Let Pn Be The Vector Space Of Polynomials Of Degree No More Than N Define The Linear Trans 1 (40.9 KiB) Viewed 12 times

Problem 3. (20=10+10 points) Let Pn be the vector space of polynomials of degree no more than n. Define the linear transformation T on P₂ by T(p(t)) = p'(t)(t+1) where p'(t) is the derivative of p(t) (you are given the fact that this is a linear transformation on P₂). (1) Let B = {1, t, t2} be the standard basis of P₂. Compute [T]B, the matrix for T relative to B. (2) Show that 2 is an eigenvalue of T, and find a corresponding eigenvector.